I must confess, I didn't read all the OP's post about his suggested method, but when I got to the part describing a battery-based source of AC, I stopped reading. The question is why supply any audio equipment with AC, when the first thing it does is convert it into DC? No audio circuit needs AC so I see no advantage of starting with DC (the battery), then converting to AC, and then the amp or other deice converts it back to DC!
Isn't it a better solution to use the DC of the battery to directly supply the circuit boards within the amp or other component? This means doing away with the DC to AC converter in the battery box and doing away with the AC to DC converter (the power supply) in the amplifier. No AC = no chance of mains-borne hum.
In practice, this needs messing with the amplifier and ensuring the battery voltage meets the requirement of the audio boards in the amp. Nothing is impossible, but is it really worth the effort and cost? I had a battery-powered amplifier for a while (from Red Wine Audio) that was designed in the first place to run on 12 V DC. Lots of common sense in this method, though they used a somewhat primitive Class D technology that let it down, sound quality-wise. I'd commend this method in theory, though no big brand goes that route.
I have never experienced any problem by using the conventional means of supplying the audio kit with AC directly from the domestic 240 V AC supply and relying on the good engineering within the amplifier to ensure the conversion to DC is done well and that undesirables such as RFI are prevented from doing damage to the signal. All good quality equipment should offer this and the only worthwhile precaution is to use a good quality screened cable between the wall socket and the amp's power input socket - something like Belden 19364. No need to pay daft prices for anything fancier as it'll add nothing to improve sound quality.
That's my experience - others may differ